Dear PSE users and moderators,
I’m new here in PSE, but I really need your help. There was this person who gave me a black envelope consisting 10+1 pages of puzzles, and also a scribble saying: “Find our favorites and you will be accepted to join our ‘pyramid cult’. Feel free to ask for help from your beloved friends on PSE. They will surely guide you into all the truth.” I’m also a newbie on grid puzzles, so, could you please give me any hint to solve these? It’s getting harder and harder later on..
- athin

1 Answer
1

First of all, any pairs of 0 and 2 can be filled since the 2 only has two sides available. Also, the 1/1 in the bottom right corner cannot reach the corner without using two sides of the 1, so fill in the only possibility left. Also, all pairs of 2 and 2 have to have the line between them filled (otherwise completing the 2s would make a closed loop). Fill these in first.

Now, let's look at the top corner. The right-hand side of the loop can not touch the 0, so only one way to go. After that, the left-hand side only has one option to avoid touching the already-completed 1 below it or creating a loop with the right-hand side. After that, the right-hand side needs to continue straight in order to avoid making a loop.

On the left side of the top corner, the line coming from the 0/2 has to connect to the upper loop's left-hand side in order to avoid filling a second side of the 1. Also, we can continue the left-hand side of that same line downward because the only other option would hit a 0.

In the bottom-left corner now, the left-hand side of the line has to continue up. Also, the right-hand side only has one option to avoid hitting the 0.

In the bottom-right corner, both sides need to continue along the border to avoid filling more sides of the 1. Also, whenever we approach the corner of a 2 like we do here, we can fill in the opposite side. (If that side was not filled, we would be branching the loop into two directions at that point.)

Neither of the lines marked red can be filled, because either of them would make it impossible to complete the two 2s.

That leaves only one way to continue the line from the bottom-left corner.

The 1 near the bottom-left corner only has one option to be filled without touching the filled line at the bottom. From there, the line only has one option to avoid the 0 and the already-filled 2 next to it.

The pair of 2s near the bottom-left corner can be filled now, and this leaves only one way to complete the 2 above and to the right of it.

Near the top corner, the line passes through one corner of the 1 below it. Since we can not draw a third line into that same corner, we have to fill in the opposite side of the 1. This leaves only one way to fill in the 2 below.

The 1 to the left of the previous ones only has one option available. After that, the line can only continue in one direction, and that is to join with the line below it.

The left-hand line of the top corner can only continue in one direction without making a 3-way intersection. From here we see that the 2 below has only one option available, so the lines must join here.

There is no way to reach the circled point without either hitting the line above or filling two sides of the 1 below.

Since we can't get to this point, we only have one option to fill the 1. This line has only one option in both directions, so fill those in as well. Now we've solved the entire bottom-left corner.

Let's look at the bottom-right corner. The 2 can only be completed in one way. That leaves only one way to continue the upper of the two line ends. And after filling that in, the bottom-most line now only has one option.

Since the circled point cannot be revisited, there is only one way to complete both of the 1s touching it.

We need to continue upwards on the right-hand border because the 1 below is already complete. From there, the line can't go to the centre of the three 0s because it has no legal way to continue from there. So we need to continue up the right-hand border.

The upper part of the small line below the top corner can only go right. After that, we can't go right because we'd leave the line above uncompletable. We also can't go down and to the right because there's no way to go after that (except again by leaving the line above hanging). So we need to go up and to the right to connect with the line above. This leaves only one way to continue the line just below on the right-hand border, and that connects with the other line near the middle.

There is only one way to complete the 2 near the bottom-right corner, and only one way to proceed from there. This completes both of the remaining 1s as well.

The line cannot go down and to the left, because we'd make two separate loops. So we go to down and to the right, leaving exactly one way to connect the lines at the bottom. Then just connect the remaining ends in the only way possible, and we get the final solution.